CH437 CLASS 10
NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 4
Synopsis. Spin-spin coupling: JHH and its magnitude. Influence of operating frequency on AB spinspin coupling pattern. Shift reagents. Spin decoupling.
NMR Coupling Constants
Spin-spin splitting and the accompanying coupling constants are important
features of NMR spectra, particularly those between protons in
1H
NMR
spectroscopy. The major naming conventions for coupling constants use the
letter J, with a number written as a superscript to the left indicating the number of
bonds between the coupling nuclei, and other information written as a subscript
(or in paretheses) on the right, as shown in the following examples.
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1
H
C
1H
C
1
13
JCH
C
13
C
1J
CC
1H
1H
1H
C
C
C
2
JHCC
or
3
2
JHC
H
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C
1H
2
JHCH
or simply
2
JHH
JHCCH
or
3
JHH
Vicinal Coupling Constants (3JHH)
For vicinal protons, the magnitude of the coupling constant (3JHH) depends upon
their spacial relationship, especially their dihedral angle (), as described by the
Karplus equation (equation (1)):
1
0
H
8.5 cos2 - 0.28 for 0o <  < 90o
9.5 cos2 - 0.28 for 90o <  < 180o
J =
H
.............................................................(1)
Typical values:
H
H
H
H
gauche ( = 60o)
anti (= 180o)
J = 2 - 6 Hz
J = 5 -14 Hz
In cycloalkanes, such as cylcohexane derivatives, vicinal coupling constants
depend on the nature of the coupling protons (i.e. equatorial-equatorial,
equatorial-axial or axial-axial), according to the Karplus equation:
Heq
X
H eq
JHH
0-5 Hz
X
Y
H eq
Y
3
Hax
Hax
X
Hax
Y
1-6 Hz
8-13 Hz
Ring-flipping in flexible cyclohexane and similar ring systems averages eq-eq/axax couplings to 4-9 Hz and eq-ax/ax-eq couplings to 1-6 Hz, but the above
values hold for more rigid analogs.
Note that in cyclopropane systems, Jcis ( = 0o) is higher than Jtrans ( = 120o):
2
Jcis = 9.0 Hz
H
H
H
H
Jtrans = 5.6 Hz
For alkene protons, a similar relationship holds, except the coupling constants
tend to be larger. Note the generally greater coupling between trans protons.
(See also acrylonitrile, Class 9).
3
J = 2 - 15 Hz
H
H
C
2
J = 0 -7 Hz
C
H
3
J = 10 - 21 Hz
For all the above examples, the variation in the quoted coupling constants is
mainly due to differing electronegativities of proximate atoms: generally,
electronegative substituents attached to the same carbon atom as vicinally
coupled protons reduce the value of 3JHH.
Vicinal coupling constants in cyclic systems also vary with the extent of ring
strain: 3JHH is lower for more highly strained rings, as shown below.
HA
HA
X
HB
3JH H ~ 2.5 - 4.0 Hz
A B
X
HB
3JH H ~ 9 - 11 Hz
A B
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Similarly, 3JHH falls off with increasing bond distance between the coupling
protons, as witnessed by comparison of a typical ortho coupling constant with the
typical cis coupling constant of alkenes (see above).
H
Jortho ~ 8 Hz
Ho
X
Geminal Coupling Constants (2JHH)
As noted in class 9, geminal protons undergo spin-spin coupling, although this
will only be actually seen (as doublets) if the protons are magnetically nonequivalent. Geminal coupling constants 2JHH are fundamentally of negative sign
(3JHH is positive), although when quoting 2JHH, the negative sign is sometimes
dropped.
H
H
C
H
C
H
C
1H
Energy
H
H
C
H
C
H
spin
electron
spin
C
Vicinal
Geminal
This is because of a combination of the energetic preference for unpaired
electron spins for electrons proximate to the same carbon atom and for electron
and nuclear spin to be paired when in proximity. Some examples of 2JHH are
given below. The geminal protons are equivalent for each of these (except the
alkene example), hence
2J
HH
is evaluated by chemical substitution of
2H
(deuterium) for 1H, measuring 2JHD and using the equation 2JHH = 6.55 2JHD.
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O
H
H
H
CH
O
H
H
CN
H
H
O
R
C
H
H
O
H
O
H
C
C
R'
O
H
O
2JHH
/Hz
_ 16.2
_ 21.5
Hyperconjugative electron
withdrawal from C-H due
to bonds
_
_ 3 to +3, depending
~0
5
on R and R',
typically ~ _2
Hyperconjugative electron
donation from O lone pairs
to C-H
+42, due to
effective O lone
pair donation
Ring size
Long Range Coupling Constants
Long-range coupling constants (4JHH and higher) are (with few exceptions) small,
lying in the range 0 – 3 Hz. This is because the spin-spin interactions are weak,
as a result of the existence of at least four bonds between the two nuclei.
However, long-range coupling is often observed for cases where two or more of
the intervening atoms belong to a -bonded system. This is the case with allylic,
homoallylic and various couplings associated with benzene rings, as illustrated
below.
CH
CH
CH
CH
Allylic couplings
4J
HH = 0 - 3 Hz
C
C
CH
Homoallylic couplings
= 0 - 2 Hz
5J
HH
CH3
Ho
4J
HH
5J
HH
Hm
Hp
0 - 1 Hz (usually
unresolved)
6J
HH
Methyl-benzene ring proton couplings
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Also, closer inspection of the 1H spectra para-disubstituted benzene derivatives
reveals additional lines: these arise from long-range aromatic proton-proton
couplings. An example is shown below.
In saturated systems, long-range coupling is not usually observed, except when
the coupling protons are held in a “W” configuration (in rigid systems) as
indicated by the heavy outline in the examples below.
H
H
4J
HH =
H
7 - 8 Hz
H
4J
HH =
1 - 2 Hz
It is emphasized that the long-range coupling constants for the above two
examples are quite exceptional.
Influence of Operating Frequency on AB Spin-Spin Splitting Pattern
For AB systems, where A and B are very different (/J ration is large: this is
strictly an AX system, see diagram below), the following two equations hold:
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JAB = 2 - 1 = 4 - 1
(2)
A - B = [(4 - 3)/2] – [(2 - 1)/2]
(3)
B
A
2  1
4 3
However, if A ~ B (/J ratio is small), then the frequency difference expression
(2) holds as before, but equation (3) does not: A and B are no longer given by
the mid point between lines 3 and 4 (A), and lines 1 and 2 (B). Instead, the line
pattern is distorted (see class 9) with A and B lying closer to the two central
lines. See diagram below.
B
A
3
4
2
1
Now,
A _ B
=
4 _ 1
3 _  2
(4)
,
and the relative intensities of the lines can be calculated from
I2
I1
=
I3
I4
=
4 _ 1
3
2
(5)
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For example, suppose we have the following spectrum, run at 60 MHz, where JAB
= 15 Hz.
3 2
B
A
4
/Hz
1
80
48
65 63
From equation (5),
I2
=
I1
I3
I4
=
80 _ 48
65 _ 63
=
16
and from equation (4),
A _ B
=
80 _ 48
65 _ 63
= 8Hz
Now, A and B will be situated symmetrically about 2 and 3, hence
A = 68 Hz and B = 60 Hz.
For the same spin-spin coupled system at 400 MHz operating frequency, A =
453 Hz and B = 400 Hz (JAB is still 15 Hz). Similar calculations as above give
(from equation (4)), 1 = 394, 2 = 409, 3 = 445, 4 = 460 Hz and (from equation
(5)), I2/I1 = I3/I4 ~ 1.8. In other words, the spectrum more closely resembles an AB
spectrum where the chemical shifts of A and B are more widely separated. In
particular, the intensity of the two satellite lines is about half of that of the inner
lines.
This example serves to illustrate that spin-spin coupling patterns are much
easier to interpret when the NMR spectrum is run at the highest possible
operating frequency.
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Shift Reagents
In the days before ultra high resolution FTNMR, standard proton spectra were
run on machines that operated at 100 MHz and often suffered from overlapping
signals (due to similar chemical shifts) and also from second-order spin-spin
splitting complexity (again due to chemical similarity of interacting protons). In
such cases, it was discovered that the presence of a complexed paramagnetic
metal ion (particularly of a “Lanthanide” element, such as Er, Eu or Pr) often
resulted in a much larger spread of chemical shifts in the 1H NMR spectrum
under investigation. This is because of the formation of loose complexes
between the agent (a “lanthanide shift reagent”) and the analyte: the chemical
shift of protons in the analyte are influenced by the paramagnetic field according
to their distances from the ion in the loose complex. Because Eu (III) is
paramagnetic, it has a short electron-spin relaxation time (<10-12 s) and so is able
to induce proton NMR shifts without appreciable line broadening. One of the
earliest shift reagents was Eu(dpm)3, as illustrated in the example below.
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Shifts are induced according to the McConnell-Robertson equation:
 =
K
3cos  _ 1
r3
H
R
C
O
r

Eu
Nowadays, with FTNMR spectrometers operating at 400-600 MHz (and higher),
there is less need for shift reagents, except for a very useful development that
uses chiral lanthanide complexes, known as chiral shift reagents. Because of
the chirality of these reagents, the chemical shifts of like protons in different
diastereoisomers and in two enantiomers are enhanced to different extents. For
example, the norbornene derivative below can exist as both exo and endo forms,
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each of which exists as a pair of enantiomers, giving (+)-exo, (-)-exo, (+)-endo
and (-)-endo.
CHO
CH3
CH3
CHO
exo
endo
CF2CF2CF3
O
O
3
Eu
Eu(hfc)3
Europium tris[3-(heptafluoropropylhydroxymethylene)-(+)-camphorate]
The 1H NMR spectrum of an endo-exo preparation, on the basis of the aldehyde
signals at ca. 9.5 ppm, clearly shows the (expected) predomination of the exo
diastereoisomer (below), but no differentiation is seen between aldehyde protons
in the enantiomers of either diastereoisomer, since the NMR probe is isotropic.
However, on addition of Eu(hfc)3 (see above), not only are the endo and exo
CHO signals are shifted by different amounts downfield, but are resolved into
doublets, indicating that the sample is racemic. When the norbornene aldehyde
complexes with Eu(hfc)3, the protons in each enantiomer experience different
magnetic fields due to the chirality of the chiral shift reagent. Thus chiral shift
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reagents can be used to check both diasteroisomeric and enantiomeric purity.
Spin Decoupling
Although spin-spin splitting gives very useful information for structure
determination, excessive splitting leads to low signal-to-noise ratios and it is
sometimes difficult to see all the lines and hence determine for certain the
multiplicity. An example is seen in the 1H NMR of HC(CH2CH3)3 below.
The process of removing magnetic coupling between spins is called decoupling
and is achieved by the application of a saturation radiofrequency pulse at the
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frequency of one of the nuclei that it is wished to decouple. The saturation pulse
is a relatively low power field (B1) left on long enough to ensure the
disappearance of all magnetization concerning that particular nucleus. If it is
applied along x’, the nuclear magnetization rotates about that axis several times
and T2 processes cause the magnetization (along y’ and z axes) to dephase, so
that the net magnetization at the end of the pulse is zero. This means that this
nucleus cannot couple with others. Because B1 is long, its frequency range is
narrow and it can be set to coincide with any of the proton sets in the above
example (i.e. with CH or CH2 or CH3). Part (or all) spin-spin coupling collapses,
leading to a simpler spectrum with enhanced signal intensities. This is illustrated
for HC(CH2CH3)3 below. Spin decoupling also gives information on which nuclei
are interacting, but nowadays there are more sophisticated ways of determining
this (see COSY, class 17).
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